请编写完整代码

好的，以下是基于MPI的Jacobi迭代求解拉普拉斯方程的完整代码：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <mpi.h>

#define ROWS 1000
#define COLS 1000
#define EPSILON 0.001
#define MAX_ITERATIONS 10000

int main(int argc, char **argv) {
    int rank, size;
    MPI_Status status;
    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &size);

    // 计算本地区域的开始和结束行号
    int local_rows = ROWS / size;
    int start_row = rank * local_rows;
    int end_row = (rank + 1) * local_rows - 1;

    // 初始化本地数组
    double **u = (double **)malloc((local_rows + 2) * sizeof(double *));
    double **u_new = (double **)malloc((local_rows + 2) * sizeof(double *));
    for (int i = 0; i < local_rows + 2; i++) {
        u[i] = (double *)malloc(COLS * sizeof(double));
        u_new[i] = (double *)malloc(COLS * sizeof(double));
        for (int j = 0; j < COLS; j++) {
            u[i][j] = 0.0;
            u_new[i][j] = 0.0;
        }
    }

    // 计算本地数组的边界
    double left_boundary, right_boundary;
    if (rank == 0) {
        left_boundary = 1.0;
        right_boundary = 0.0;
    } else if (rank == size - 1) {
        left_boundary = 0.0;
        right_boundary = 1.0;
    } else {
        left_boundary = 0.0;
        right_boundary = 0.0;
    }

    // 进行Jacobi迭代计算
    double diff, global_diff;
    int iterations = 0;
    do {
        // 交换边界数据
        if (rank > 0) {
            MPI_Sendrecv(u[1], COLS, MPI_DOUBLE, rank - 1, 0, u_new[0], COLS, MPI_DOUBLE, rank - 1, 0, MPI_COMM_WORLD, &status);
        }
        if (rank < size - 1) {
            MPI_Sendrecv(u[local_rows], COLS, MPI_DOUBLE, rank + 1, 0, u_new[local_rows + 1], COLS, MPI_DOUBLE, rank + 1, 0, MPI_COMM_WORLD, &status);
        }

        // 进行Jacobi迭代计算
        diff = 0.0;
        for (int i = 1; i <= local_rows; i++) {
            for (int j = 1; j < COLS - 1; j++) {
                u_new[i][j] = 0.25 * (u[i - 1][j] + u[i + 1][j] + u[i][j - 1] + u[i][j + 1]);
                if (i == 1) u_new[i - 1][j] = left_boundary;
                if (i == local_rows) u_new[i + 1][j] = right_boundary;
                diff += fabs(u_new[i][j] - u[i][j]);
            }
        }

        // 更新本地数组
        for (int i = 1; i <= local_rows; i++) {
            for (int j = 1; j < COLS - 1; j++) {
                u[i][j] = u_new[i][j];
            }
        }

        // 计算全局误差
        MPI_Allreduce(&diff, &global_diff, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);

        // 增加迭代次数
        iterations++;
    } while (global_diff > EPSILON && iterations < MAX_ITERATIONS);

    // 输出结果
    if (rank == 0) {
        printf("Iterations: %d\n", iterations);
        printf("Solution:\n");
        for (int i = 1; i <= local_rows; i++) {
            for (int j = 0; j < COLS; j++) {
                printf("%f ", u[i][j]);
            }
            printf("\n");
        }
    }

    // 释放本地数组
    for (int i = 0; i < local_rows + 2; i++) {
        free(u[i]);
        free(u_new[i]);
    }
    free(u);
    free(u_new);

    MPI_Finalize();
    return 0;
}

在程序中，我们使用了MPI_Sendrecv()函数进行边界数据的交换，使用MPI_Allreduce()函数计算全局误差。在输出结果时，我们只在rank为0的进程上输出。

另外，由于我们使用了动态内存分配，需要在程序结束时释放内存。

希望可以帮助您解决问题，有任何疑问欢迎继续追问！